$\dfrac{ 7s + 9t }{ 2 } = \dfrac{ 6s + 4u }{ -9 }$ Solve for $s$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 7s + 9t }{ {2} } = \dfrac{ 6s + 4u }{ -9 }$ ${2} \cdot \dfrac{ 7s + 9t }{ {2} } = {2} \cdot \dfrac{ 6s + 4u }{ -9 }$ $7s + 9t = {2} \cdot \dfrac { 6s + 4u }{ -9 }$ Multiply both sides by the right denominator. $7s + 9t = 2 \cdot \dfrac{ 6s + 4u }{ -{9} }$ $-{9} \cdot \left( 7s + 9t \right) = -{9} \cdot 2 \cdot \dfrac{ 6s + 4u }{ -{9} }$ $-{9} \cdot \left( 7s + 9t \right) = 2 \cdot \left( 6s + 4u \right)$ Distribute both sides $-{9} \cdot \left( 7s + 9t \right) = {2} \cdot \left( 6s + 4u \right)$ $-{63}s - {81}t = {12}s + {8}u$ Combine $s$ terms on the left. $-{63s} - 81t = {12s} + 8u$ $-{75s} - 81t = 8u$ Move the $t$ term to the right. $-75s - {81t} = 8u$ $-75s = 8u + {81t}$ Isolate $s$ by dividing both sides by its coefficient. $-{75}s = 8u + 81t$ $s = \dfrac{ 8u + 81t }{ -{75} }$ Swap signs so the denominator isn't negative. $s = \dfrac{ -{8}u - {81}t }{ {75} }$